1. Model update

Previously, we model all the 8 help indicators together using a cross-sectional model. Now, we try to model the financial help from other 7 practical helps seperately.



The financial help part is parameterized as follows: \[ P(Y_{i,J+1}^{TP}\mid \boldsymbol{x}_i) = P(Y^{TP*}_{i,J+1}>0),\\ Y^{TP*}_{i,J+1} = \boldsymbol{u}_{tp}^T \boldsymbol{x}_i + \epsilon_i^{TP} \] \[ \boldsymbol{u}_{tp} = (u^{tp}_1, \ldots, u^{tp}_K)\\ u^{tp}_k\sim N(0, \sigma_{u_{tp}}^2),\ \text{for}\ k=1,\ldots,K\\ \sigma_{u_{tp}}^2 \sim IG(1.5, 0.01) \] Note that an intercept is included in \(\boldsymbol{u}_{tp}^T \boldsymbol{x}_i\). And inverse-gamma(1.5, 0.01) is choosen because we want variances prior to be non-informative and inverse-gamma(0.01, 0.01) does not work in empty model case.

2. Fit empty and full model to the dataset

library(jsem)
#> Loading required package: coda
#> jsem 0.1 using 3 threads (see ?getjsem_threads())
load("jags.rda")
aidrp_data_simple <- list(ytp=jags.data$ytp, yfp = jags.data$yfp, xi=xi.start,
                          female = jags.data$female,
                          distlong = jags.data$distlong,
                          age40 = jags.data$age40,
                          partner = jags.data$partner,
                          clt2 = jags.data$clt2,
                          c2to4 = jags.data$c2to4,
                          c5to10 = jags.data$c5to10,
                          c11to16 = jags.data$c11to16,
                          cgt16 = jags.data$cgt16,
                          jbs3 = jags.data$jbs == 3,
                          jbs4 = jags.data$jbs == 4,
                          page70 = jags.data$page70,
                          plive = jags.data$plive %in% c(3, 4, 5, 7, 9))

dylanie_empty_res <- dylanie_model_fin_sep_simple(~1, data=aidrp_data_simple, 
                                                  mcmc_len = 7500, verbose = T)
round(dylanie_sep_fin_summary(dylanie_empty_res, burnin = 2500)$statistics,2)

dylanie_full_res <- dylanie_model_fin_sep_simple(~female + distlong + age40 + partner + 
                                                   clt2 + c2to4 + c5to10 + c11to16 + 
                                                   cgt16 + jbs3 + jbs4 + page70 + plive,
                                                 data=aidrp_data_simple, 
                                                 mcmc_len = 7500, verbose = T)
round(dylanie_sep_fin_summary(dylanie_full_res, burnin = 2500)$statistics,2)

2.1 Empty model result

Mean SD Naive.SE Time.series.SE
g[1,1] 0.00 0.00 0.00 0.00
g[1,2] 0.03 0.11 0.00 0.01
g[1,3] -0.37 0.20 0.00 0.04
g[1,4] 1.62 0.08 0.00 0.01
b_tp[1] -1.96 0.06 0.00 0.01
b_fp[1] -4.88 0.07 0.00 0.01
u_tp[1] -2.70 0.03 0.00 0.00
u_fp[1] -1.90 0.02 0.00 0.00
sig2_tp 2.91 0.13 0.00 0.02
sig2_fp 3.69 0.17 0.00 0.02
sig2_u_tp 3.69 7.42 0.10 0.10
sig2_u_fp 1.75 2.63 0.04 0.04
rho 0.23 0.03 0.00 0.00
p[1] 0.13 0.01 0.00 0.00
p[2] 0.13 0.01 0.00 0.00
p[3] 0.09 0.02 0.00 0.00
p[4] 0.65 0.02 0.00 0.00

2.2 Full model result

Mean SD Naive.SE Time.series.SE
b_tp_intercept -2.27 0.07 0 0.01
b_tp_female 0.83 0.05 0 0.00
b_tp_distlong -0.82 0.07 0 0.01
b_tp_age40 0.00 0.00 0 0.00
b_tp_partner -0.26 0.06 0 0.00
b_tp_clt2 -0.18 0.10 0 0.00
b_tp_c2to4 -0.23 0.08 0 0.00
b_tp_c5to10 0.00 0.06 0 0.00
b_tp_c11to16 0.06 0.06 0 0.00
b_tp_cgt16 0.13 0.06 0 0.00
b_tp_jbs3 0.38 0.13 0 0.01
b_tp_jbs4 0.50 0.06 0 0.00
b_tp_page70 0.03 0.00 0 0.00
b_tp_plive 0.58 0.05 0 0.00
b_fp_intercept -4.00 0.08 0 0.01
b_fp_female 0.75 0.06 0 0.00
b_fp_distlong -0.12 0.09 0 0.01
b_fp_age40 -0.05 0.01 0 0.00
b_fp_partner -0.64 0.07 0 0.00
b_fp_clt2 -0.19 0.08 0 0.00
b_fp_c2to4 -0.31 0.07 0 0.00
b_fp_c5to10 -0.13 0.06 0 0.00
b_fp_c11to16 -0.10 0.07 0 0.00
b_fp_cgt16 -0.09 0.11 0 0.01
b_fp_jbs3 0.47 0.14 0 0.01
b_fp_jbs4 0.26 0.08 0 0.00
b_fp_page70 0.00 0.01 0 0.00
b_fp_plive -0.28 0.06 0 0.00
u_tp_intercept -2.90 0.10 0 0.01
u_tp_female -0.07 0.07 0 0.00
u_tp_distlong -0.13 0.08 0 0.00
u_tp_age40 0.00 0.01 0 0.00
u_tp_partner -0.14 0.08 0 0.00
u_tp_clt2 0.05 0.14 0 0.00
u_tp_c2to4 0.00 0.11 0 0.00
u_tp_c5to10 0.19 0.09 0 0.00
u_tp_c11to16 0.00 0.09 0 0.00
u_tp_cgt16 0.01 0.09 0 0.00
u_tp_jbs3 -0.07 0.18 0 0.00
u_tp_jbs4 -0.02 0.09 0 0.00
u_tp_page70 0.01 0.01 0 0.00
u_tp_plive 0.65 0.07 0 0.00
u_fp_ intercept -1.54 0.06 0 0.00
u_fp_ female 0.19 0.05 0 0.00
u_fp_ distlong -0.25 0.06 0 0.00
u_fp_ age40 -0.07 0.00 0 0.00
u_fp_ partner -0.67 0.06 0 0.00
u_fp_ clt2 -0.06 0.09 0 0.00
u_fp_ c2to4 -0.06 0.07 0 0.00
u_fp_ c5to10 0.12 0.06 0 0.00
u_fp_ c11to16 0.14 0.06 0 0.00
u_fp_ cgt16 0.01 0.08 0 0.00
u_fp_ jbs3 0.28 0.11 0 0.00
u_fp_ jbs4 0.16 0.06 0 0.00
u_fp_ page70 0.02 0.00 0 0.00
u_fp_ plive 0.05 0.05 0 0.00
sig2_tp 1.99 0.08 0 0.01
sig2_fp 2.17 0.10 0 0.01
sig2_u_tp 0.75 0.33 0 0.01
sig2_u_fp 0.26 0.12 0 0.00
rho 0.49 0.02 0 0.00
p[1] 0.18 0.02 0 0.00
p[2] 0.11 0.02 0 0.00
p[3] 0.05 0.01 0 0.00
p[4] 0.67 0.03 0 0.00

2.3 Several comments on the results

  1. For to parent helps
    • partner has a coefficient of -0.14(0.08) for financial help, and -0.26(0.06) for practicle helps;
    • plive has a coefficient of 0.65(0.07) for financial help, and a coefficient of 0.58(0.05) for practicle helps;
  2. For from parent helps
    • female has a coefficient of 0.19(0.05) for financial help, and 0.75(0.06) for practicle helps;
    • age40 has a coefficient of -0.07(0.00) for financial help, and -0.05(0.01) for practicle helps;
    • partner has a coefficient of -0.67(0.06) for financial help, and -0.64(0.07) for practicle helps;

3. Some statistics about \(Y_{i,J+1}^{TP}\) and \(Y_{i,J+1}^{FP}\)

There is no missing data for financial responses.

load("~/Dropbox/Projs/Files for Siliang/WP1 methods and analysis/jags.rda")
table(jags.data$ytp[,8])
## 
##     0     1 
## 13927   933
table(jags.data$yfp[,8])
## 
##     0     1 
## 12921  1939

4. Modeling correlations between financial helps and practical helps

4.1 Diagram



4.2 Parameterization

We extend the previous parameterization of correlation between practical to/from parents helps as follows,

For \(i=1,...,N\), \[ \eta_i^{TP} = \boldsymbol{x}_i^T \boldsymbol{b}_{tp} + \epsilon_{i,1}\\ \eta_i^{FP} = \boldsymbol{x}_i^T \boldsymbol{b}_{fp} + \epsilon_{i,2}\\ \phi_i^{TP} = \boldsymbol{x}_i^T \boldsymbol{u}_{tp} + \epsilon_{i,3}\\ \phi_i^{FP} = \boldsymbol{x}_i^T \boldsymbol{u}_{fp} + \epsilon_{i,4}\\ \begin{bmatrix} \epsilon_{i,1}\\ \epsilon_{i,2}\\ \epsilon_{i,3}\\ \epsilon_{i,4} \end{bmatrix}\sim N\left( \boldsymbol{0}, \begin{bmatrix} \sigma_{tp}^2 & \rho_1\sigma_{tp}\sigma_{fp} & \rho_2\sigma_{tp} & \rho_3\sigma_{tp}\\ \rho_1\sigma_{tp}\sigma_{fp} & \sigma_{fp}^2 & \rho_4\sigma_{fp} & \rho_5\sigma_{fp}\\ \rho_2\sigma_{tp} & \rho_4\sigma_{fp} & 1 & \rho_6 \\ \rho_3\sigma_{tp} & \rho_5\sigma_{fp} & \rho_6 & 1 \end{bmatrix}\right),\\ \eta^{TP'}_i = \boldsymbol{x}_i^T\boldsymbol{b}_{tp} + \epsilon_{tp},\ \epsilon_{tp}\sim N(0, \sigma_{tp}^2),\\ \eta^{FP'}_i = \boldsymbol{x}_i^T\boldsymbol{b}_{fp} + \epsilon_{fp},\ \epsilon_{fp}\sim N(0, \sigma_{fp}^2) \]

And for \(i=1,...,N\), \[ P(Y^{TP}_{i,J+1}=1\mid \boldsymbol{x}_i) = P(\phi_i^{TP}>0)\\ P(Y^{FP}_{i,J+1}=1\mid \boldsymbol{x}_i) = P(\phi_i^{FP}>0) \]

Then for \(\xi_i=4\), \[ P(Y^{TP}_{i,j}=1\mid \boldsymbol{x}_i) = \text{logistic} (\alpha_j + \beta_j\eta^{TP}_i)\\ P(Y^{FP}_{i,j}=1\mid \boldsymbol{x}_i) = \text{logistic}(\alpha_j + \beta_j\eta^{FP}_i), \] For \(\xi_i=2\), \[ P(Y^{FP}_{i,j}=1\mid \boldsymbol{x}_i) = \text{logistic}(\alpha_j + \beta_j\eta^{FP'}_i) \] For \(\xi_i=3\), \[ P(Y^{TP}_{i,j}=1\mid \boldsymbol{x}_i) = \text{logistic}(\alpha_j + \beta_j\eta^{TP'}_i) \]

4.3 Results

4.3.1 Correlations

##      Mean   SD
## [1,] 0.48 0.02
## [2,] 0.61 0.02
## [3,] 0.32 0.02
## [4,] 0.20 0.03
## [5,] 0.57 0.02
## [6,] 0.02 0.02

4.3.2 Compare coefficients with previous model.

b_tp
Mean.old Mean.new SD.old SD.new
intercept -2.35 -2.81 0.06 0.08
female 0.84 0.84 0.05 0.05
distlong -1.09 -0.90 0.07 0.08
age40 0.00 0.00 0.00 0.00
partner -0.27 -0.24 0.05 0.06
clt2 -0.14 -0.23 0.09 0.08
c2to4 -0.21 -0.19 0.08 0.07
c5to10 0.04 0.02 0.06 0.06
c11to16 0.05 0.04 0.06 0.07
cgt16 0.12 0.14 0.06 0.06
jbs3 0.35 0.36 0.13 0.12
jbs4 0.45 0.52 0.06 0.07
page70 0.03 0.04 0.00 0.00
plive 0.58 0.73 0.05 0.05
b_fp
Mean.old Mean.new SD.old SD.new
intercept -4.22 -4.34 0.09 0.08
female 0.75 0.78 0.06 0.06
distlong -0.42 -0.32 0.08 0.08
age40 -0.05 -0.06 0.01 0.01
partner -0.67 -0.74 0.07 0.07
clt2 -0.14 -0.12 0.09 0.09
c2to4 -0.25 -0.20 0.07 0.07
c5to10 -0.07 -0.03 0.07 0.07
c11to16 -0.07 -0.07 0.07 0.07
cgt16 -0.16 -0.20 0.10 0.10
jbs3 0.43 0.38 0.14 0.14
jbs4 0.23 0.20 0.07 0.08
page70 0.00 0.00 0.00 0.01
plive -0.34 -0.32 0.06 0.06

4.3.3 Standardized coefficients for practical help and financial help

PTP.coef FTP.coef PTP.sd FTP.sd
intercept -0.87 -0.97 0.08 0.04
female 0.26 -0.01 0.05 0.03
distlong -0.28 -0.03 0.08 0.04
age40 0.00 0.00 0.00 0.00
partner -0.07 -0.03 0.06 0.04
clt2 -0.07 0.01 0.08 0.06
c2to4 -0.06 0.00 0.07 0.05
c5to10 0.01 0.06 0.06 0.04
c11to16 0.01 0.00 0.07 0.04
cgt16 0.04 0.00 0.06 0.04
jbs3 0.11 -0.03 0.12 0.08
jbs4 0.16 -0.01 0.07 0.04
page70 0.01 0.00 0.00 0.00
plive 0.22 0.21 0.05 0.03
PFP.coef FFP.coef PFP.sd FFP.sd
intercept -0.96 -0.89 0.08 0.03
female 0.17 0.12 0.06 0.03
distlong -0.07 -0.14 0.08 0.03
age40 -0.01 -0.04 0.01 0.00
partner -0.16 -0.35 0.07 0.03
clt2 -0.03 -0.03 0.09 0.05
c2to4 -0.04 -0.03 0.07 0.04
c5to10 -0.01 0.06 0.07 0.03
c11to16 -0.02 0.06 0.07 0.03
cgt16 -0.04 0.01 0.10 0.04
jbs3 0.08 0.16 0.14 0.06
jbs4 0.04 0.07 0.08 0.03
page70 0.00 0.01 0.01 0.00
plive -0.07 0.05 0.06 0.03

4.3.4 Additional MCMC chains plots

b_tp

b_fp

u_tp

u_fp